Neural Network dan Logika Kabur

Neural networks and fuzzy logic are two complimentary technologies

Neural networks can learn from data and feedback

– It is difficult to develop an insight about the meaning associated with each neuron and each weight

– Viewed as “black box” approach (know what the box does but not how it is done conceptually!)

Two ways to adjust the weights using backpropagation

– Online/pattern Mode: adjusts the weights based on the error signal of one input-output pair in the trainning data.

• Example: trainning set containning 500 input-output pairs, this mode BP adjusts the weights 500 times for each time the algorithm sweeps through the trainning set. If the algorithm sweeps converges after 1000 sweeps, each weight adjusted a total of 50,000 times

– Batch mode (off-line): adjusts weights based on the error signal of the entire training set.

• Weights are adjusted once only after all the trainning data have been processed by the neural network.

• From previous example, each weight in the neural network is adjusted 1000 times.

Fuzzy rule-based models are easy to comprehend (uses linguistic terms and the structure of if-then rules)

Unlike neural networks, fuzzy logic does not come with a learning algorithm

– Learning and identification of fuzzy models need to adopt techniques from other areas

Since neural networks can learn, it is natural to marry the two technologies.

Neuro-fuzzy system can be classified into three categories: 1. A fuzzy rule-based model constructed using

a supervised NN learning technique 2. A fuzzy rule-based model constructed using

reinforcement-based learning 3. A fuzzy rule-based model constructed using

NN to construct its fuzzy partition of the input space

A class of adaptive networks that are functionally equivalent to fuzzy inference systems.

ANFIS architectures representing both the Sugeno and Tsukamoto fuzzy models

Assume - two inputs X and Y and one output Z Rule 1: If x is A1 and y is B1, then f1 = p1x + q1y +r1 Rule 2: If x is A2 and y is B2, then f2 = p2x + q2y +r2

Every node i in this layer is an adaptive node with a node function O1,i = mAi (x), for I = 1,2, or O1,i = mBi-2 (y), for I = 3,4 Where x (or y) is the input to node i and Ai (or Bi) is a linguistic label ** O1,i is the membership grade of a fuzzy set and it specifies the degree to which the given input x or y satisfies the quantifies

Typically, the membership function for a fuzzy set can be any parameterized membership function, such as triangle, trapezoidal, Guassian, or generalized Bell function.

Parameters in this layer are referred to as Antecedence Parameters

Every node i in this layer is a fixed node labeled P, whose output is the product of all the incoming signals:

O2,i = Wi = min{mAi (x) , mBi (y)}, i = 1,2 Each node output represents the firing strength of

a rule.

Every node in this layer is a fixed node labeled N. The ith node calculates the ratio of the ith rule’s firing strength to the sum of all rules’firing stregths:

O3,i = Wi = Wi /(W1+W2) , i =1,2 (normalized firing strengths]

Every node i in this layer is an adaptive node with a node function

__ __ O 4,i = wi fi = wi (pix + qiy +ri) …Consequent

parameters

The single node in this layer is a fixed node labeled S, which computes the overall output as the summation of all incoming signals:

__ O 5,1 = Si wi fi

ANFIS architecture for the Sugeno fuzzy model, weight normalization is performed at the very last layer

Equivalent ANFIS architecture using the Tsukamoto fuzzy model